Whether you drink beetroot juice or not, your skin temperature goes down about the same amount when you're in a cool room.

When you're in a cool room, you produce more saliva than when you're in a warm room, whether or not you drink beetroot juice.

When you're in a cool room, your saliva has more nitrite after drinking beetroot juice than when you're in a warm room.

When you drink beetroot juice in a cool room, your body produces more nitrite in your blood than when you drink it in a warm room.

Whether you drink beetroot juice or not, you feel equally cold when you're in a cool room.